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# Easy but interesting!

Factorize:-

x⁴-75x+100

Note by Naitik Sanghavi
2 years, 4 months ago

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By Rational Root Theorem, there's no rational roots So if it can be factored, then it must be the product of two irreducible quadratic polynomials.

$(x^2+ax+b)(x^2+cx + d)$

Because the sum of roots of this expression equals to 0, this motivates us to have $$a = - c$$.

And because the product of roots is 100, then $$bd = 100$$.

So we have

$(x^2+ ax + b)(x^2 - ax + 100/b)$

Expand and compare the coefficients gives $$(a,b) = (-5,5), (5,20 )$$.

- 2 years, 4 months ago